Finite Group DatabasebetaFinite Group Databasebeta| order | 19216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C1201 ⋊ M16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9608 |
Polycyclic presentation:
2^4,1201|a^2=c,c^2=d,b^a=bd,e^a=e^1152,e^c=e^12001210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50307914, #50307915, C2×#34063532, … |
| maximal normal subgroup of | #50307914, #50307915, C2×#34063532, … |
| maximal quotient of | #50307909, C22⋊#23751197, #50307921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19216, 49);